A non-vanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system, however no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ε = E/N , the energy per degree of freedom. The fu...

We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H = 1/4. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to B.

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-V...

Error and erasure exponents for the broadcast channel with degraded message sets are analyzed. The focus of our error probability analysis is on the main receiver where, nominally, both messages are to be decoded. A two-step decoding algorithm is proposed and analyzed. This receiver first attempts to decode both messages, failing which, it attempts to decode only the message representing the co...

If A is a primitive matrix, then there is a smallest power of A (its fully indecomposable exponent) that is fully indecomposable, and a smallest power of A (its strict fully indecomposable exponent) starting from which all powers are fully indecomposable. We obtain bounds on these two exponents.

The discovery of the self similarity of Ethernet traac at Bellcore has had a profound eeect on the world of performance modelling. This paper examines the eeects of self similarity of input traac on the performance of a queue. We use a traac characterisation due to Robert and Le Boudec which allows self similar traac with an arbitrary mean and Hurst parameter to be generated. The technique give...

We prove some multiplicity results for a class of singular quasilinear elliptic problems involving the critical Hardy-Sobolev exponent and singularities on a half-space.

We consider a queue fed by Gaussian traffic and give conditions on the input process under which the path space large deviations of the queue are governed by the rate function of the fractional Brownian motion. As an example we consider input traffic that is composed of of independent streams, each of which is a fractional Brownian motion, having different Hurst indices.

We consider the problem of efficient estimation for the drift of fractional Brownian motion B := ( B t ) t∈[0,T ] with hurst parameter H less than 1 2 . We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

introduction: the photoelectric attenuation coefficient of substances is known to depend upon the energy e of the photon and the effective atomic number of substances (zeff) as (zeff x /e y ).  no definitive values about these indices x, y are given in the literature. the index x is said to lie between, 3.0 and 4.0, while for ‘y’ different values have been assigned, between 3.0 and 4.0. methodo...